Getting to grips with fluid mechanics


This blog follows on from previous attempts trying to provide information about the new topics in the AQA AS and A-level PE specifications, trying to be helpful by providing suitable notes / explanations of each (most) of this new content

We’ve looked at venous return and vitamins and minerals; stability and Vygotsky; the history of mob Football, real Tennis and the Much Wenlock Olympic Games together with the emergence of female performers in Football, Tennis and Athletics.

Today’s effort is biomechanics! Specifically, fluid mechanics.

Many substances have different densities. Density is the mass per unit volume. Solids and liquids have many more atoms closer together than gases, they are much more dense. Fluid mechanics is the science of these less-dense substances, mainly water, but also air, which is regarded by physicists as a fluid.

Walking through air is easy because air is not very dense. Walking through water is much more difficult because water is dense. You literally have to push the water that’s in front of you out of the way; as you move forward, the water sloshes around you into the space you’ve just left behind.

It’s much easier and faster to swim through water than it is to walk through it, because you can make your body into a long, thin shape that creates less resistance. You glide through the water more smoothly, disturbing it less, and because there’s less resistance, you can move faster.

Air is a fluid, just like water, because it can move easily; it flows. Moving through air is similar to moving through water. Most fluids behave in the same way, so just like in water, in order to move quickly through air, you’re better off in a long, thin vehicle that creates as little disturbance as possible. That’s why planes and trains are tube-shaped in exactly the same way that we swim; horizontal with our bodies laid out long and thin.

Fluid mechanics is concerned with how objects move through fluids. The science involved is just the same if the object is still and the fluid moves around it. That’s why the performance of a formula one car or a cyclist can be studied in a wind tunnel.

Laminar and turbulent flow

When water is emptied out of a plastic bottle, it can be made to flow in two different ways. Tipping the bottle at a shallow angle allows the water to flow out smoothly, with air moving past the water, in the opposite direction, filling the bottle with ’empty space’, as if it were taking the water’s place in the bottle.

If the bottle is tipped more, or held vertically, the water comes out noisily, in sudden jerks. That’s because the air and the water are fighting for space at the neck of the bottle. Sometimes the water wins and it rushes out, sometimes the air wins and instead, it rushes in, briefly stopping the water flow. The fight between water leaving and air entering the bottle gives the ‘glug-glug’ sound you hear during pouring.

What is happening is the two extreme types of fluid flow. The smooth flow occurs when the water and the air slide very smoothly past each other in layers. This is called laminar flow.

When the air and water move in a more erratic way, it is called turbulent flow. In sport, the idea is to adjust the shape of the body so the flow of air around it is as smooth as possible; so it’s laminar flow rather than turbulent flow. The more turbulence there is, the more air resistance the body will experience, and the slower it will go.

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Boundary layer

The speed at which a fluid flows past an object varies according to how far from the object the fluid is.

For example, when a 100 mph wind is blowing over a stationary car, right next to the car the speed of the air is zero. This is because the attractive forces between the molecules of the car’s paintwork and the air molecules that touch them makes the air stick to the car. Further away from the car the wind speed is higher. At a certain distance from the car, the air will be travelling at its full speed of 100 mph.

The region surrounding the car where the air speed increases from zero to its maximum of 100 mph is called the boundary layer. Laminar flow occurs when the fluid can flow efficiently, gently and smoothly increasing in speed across the boundary layer. Turbulent flow happens when the fluid gets jumbled and mixed up chaotically instead of sliding past itself in smooth layers.

Drag

Drag is air (or water) resistance; it is the force that a moving body feels when the flow of air around it starts to become turbulent. Drag increases with speed, but it is not a linear relationship.

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As all cyclists will confirm, the faster you go, the harder you have to work against the air. Cyclists try to adopt a streamlined posture that disturbs the airflow as little as possible.

There are two types of drag; friction (surface) drag and form drag and they have different causes.

The air in contact with a cyclist will be stationary, but the layer just beyond that will be moving a little bit, and the layer beyond that is moving a little bit more. All these layers of air are sliding past one another and surface drag is the friction between the different layers that make up the boundary layer.

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The rougher the object, the more turbulent the air flow becomes. The more turbulent the air flow, the greater the friction between the layers, and the greater the drag. At low speeds, the flow of air splits when it meets an object and, providing the object is reasonably streamlined, flows right around it, closely following its outline. But the faster the air flow and the less aerodynamic the object, the more the air flow breaks away and becomes more turbulent. That’s what we mean by form drag.

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Because air flows round objects, following another performer can have advantages. A slipstream is a region behind a moving object where the air or water is moving at similar velocities to the moving object. ‘Slipstreaming’ or ‘drafting’ works because of the motion of the fluid in the slipstream.

A slipstream caused by turbulent flow has a slightly lower pressure than the fluid surrounding the object. When the flow is laminar, the pressure behind the object is higher than the surrounding fluid.

Because of this, the shape of an object determines how strong the slipstream effect is. A bullet-like (aerodynamic) shape causes less turbulence, creating a more laminar flow and producing a smaller and weaker slipstream. But a box-like shape will cause a reduction in pressure behind the object and a stronger slipstream.

Travelling in the slipstream of somebody means that the performer will require less power to maintain their speed than if they were moving independently. Slipstreaming in cycling is common, but also works in swimming and even running.

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Bernoulli’s principle

There is a basic law of physics called the conservation of energy, which explains that energy cannot be created or destroyed, it can only change from one form into another.

The faster a fluid is moving, the more kinetic energy it will have. But energy cannot simply be created. In order for a fast moving fluid to have more kinetic energy, it must get it from somewhere else. The extra energy comes from a reduction in the fluid’s pressure. As the fluid gets quicker, it’s pressure drops.

This is Bernoulli’s principle. The principle helps explain how aerofoils on aeroplanes work.

The upper surface of an aerofoil is curved, while the lower surface is straight. The air going above aerofoil goes faster than the air below, so the air above the aerofoil is at a lower pressure and this generates lift (upward force).

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Bernoulli’s principle explains how an upward lift force helps gain horizontal distance in the flight of a discus.

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In some sports, the requirement is not for upward lift, but for downward lift. Based on the same principle, formula one cars generate ‘downforce’. The purpose of this force is to push the car into the road to give it more grip in corners.

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The same idea is used by cyclists and speed skiers by adopting a body position that generates downward lift forces that allow faster cornering.

Questions

1. Explain how a lift force is imparted to a discus during flight and explain its effects on the flightpath of the discus. [4 marks]

2. Explain the methods used to reduce the forces acting on a cyclist whilst racing. [5 marks]

3. Describe a cyclists’ use of the Bernoulli effect to increase his speed. [6 marks]

Answers

1.
A. Body forms an aerofoil shape
B. Creating angle of attack
C. Air travels further under cyclist
D. Air travels faster under cyclist
E. Creates low pressure under cyclist
F. (Bernoulli) Force formed from high to low pressure
G. Bernoulli force downwards/down force

2.
A. Discus is an aerofoil shape
B. Takes on an appropriate angle of attack to the direction of motion
C. Air has to travel further over the top of the discus
D. Air travels faster over the top of the discus
E. This creates a low pressure area on top of the discus
F. Called the Bernoulli principle
G. Air tries to move from high to low pressure (creating the lift force)
H. Makes flight path non parabolic/asymmetrical
I. Lengthens flight path/discus travels further / is in air for longer

3.
A. Friction (between wheels and track) acts against cyclist
B. Air resistance/Fluid Friction (acting against cyclist moving through air)
C. Acts in opposite direction of motion
D. Increases as cyclist’s speed increases
E. Cyclist needs to reduce forces to achieve a higher speed/velocity
F. Reduce friction by using thin / high pressured tyres
G. Reduce friction by streamlining
H. Creating smooth flow around cyclist / reducing turbulent flow / drag reducing profile drag / turbulence behind
I. Reduce frontal / forward cross sectional area
J. Reduce surface friction of air on cyclist / specialist smooth clothing / helmet
K. Reduce turbulence behind cyclist / change body shape to smooth air flow behind cyclist

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